Transport properties of viscous fluid through moving permeable walls in fuzzy enviormnent

Abstract

The current flow phenomena characterized by several flow properties depend on their physical behavior and the geometry of the problem. The present investigation deals with the flow of viscous two-dimensional liquid through an expanding/contracting surface where the walls are moving and also permeable. The differential equation governing the two-dimensional viscous flow is also fuzzified. Here, some parameters appeared in the differential equation are considered as triangular fuzzy numbers (TFN). The fuzzified “Boundary Value Problem” (BVP) is defuzzified by using “Signed Distance Method”. Finally, numerical solutions are for both crisp and fuzzy model are obtained and presented via graphs and tables. Further, the results are obtained by employing approximate analytical technique known as “Differential Transform Method” (DTM) and the refinement of these are verified with Pade approximant of order [4/4]. Finally, the numerical simulations by using traditional numerical technique and the current approximate analytical technique are compared for both the crisp and the fuzzified solutions of the BVP showing a good correlation among themselves. Moreover, the important outcomes of the study are; the enhanced Reynolds number the flow profile augments significantly and this enhancement is observed near the first region that is closed to the lower wall of the channel but the impact is reversed in the second. The interesting fact is that for the higher wall dilation parameter the fuzzified values of the Reynolds number shows its reverse impact.